• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.10
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• pp.464-472
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• 2001

This study uses distributed parameter systems as the spatial discretization technique, modelling in lumped parameter systems, and applies fast WALSH transform and the Picard's iteration method to high order partial differential equations and matrix partial differential equations. This thesis presents a new algorithm which usefully exercises the optimal control in the distributed parameter systems. In exercising optimal control of distributed parameter systems, excellent consequences are found without using the existing decentralized control or hierarchical control method. This study will help apply to linear time-varying systems and non-linear systems. Further research on algorithm will be required to solve the problems of convergence in case of numerous applicable intervals.

• Journal of The Korean Society of Agricultural Engineers
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• v.58 no.1
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• pp.81-90
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• 2016

The Agricultural Systems Application Platform (ASAP) provides bottom-up modelling and simulation environment for agricultural engineer. The purpose of this study is to expand usability of the ASAP to the second order partial differential equations: elliptic equations, parabolic equations, and hyperbolic equations. The ASAP is a general-purpose simulation tool which express natural phenomenon with capsulized independent components to simplify implementation and maintenance. To use the ASAP in continuous problems, it is necessary to solve partial differential equations. This study shows usage of the ASAP in elliptic problem, parabolic problem, and hyperbolic problem, and solves of static heat problem, heat transfer problem, and wave problem as examples. The example problems are solved with the ASAP and Finite Difference method (FDM) for verification. The ASAP shows identical results to FDM. These applications are useful to simulate the engineering problem including equilibrium, diffusion and wave problem.

• Nuclear Engineering and Technology
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• v.55 no.8
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• pp.2952-2965
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• 2023

Advanced reactors, such as Small Modular Reactors or existing Nuclear Power Plants, often use Field Programmable Gate Array (FPGA) based controllers in new Instrumentation and Control (I&C) system architectures or as an alternative to existing analog-based I&C systems. Compared to CPU-based Programmable Logic Controllers (PLCs), FPGAs offer better overall performance. However, programming functions on FPGAs can be challenging due to the requirement for a hardware description language that does not explicitly support the operation of real numbers. This study aims to implement the Reactor Trip (RT) functions of the existing analog-based Reactor Protection System (RPS) using FPGAs. The RT equations for Overtemperature delta Temperature and Overpower delta Temperature involve dynamic compensators expressed with the Laplace transform variable, 's', which is not directly supported by FPGAs. To address this issue, the trip equations with the Laplace variable in the continuous-time domain are transformed to the discrete-time domain using the Z-transform. Additionally, a new operation based on a relative value for the equation range is introduced for the handling of real numbers in the RT functions. The proposed approach can be utilized for upgrading the existing analog-based RPS as well as digitalizing control systems in advanced reactor systems.

• East Asian mathematical journal
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• v.27 no.3
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• pp.289-297
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• 2011

The introduction of fuzzy differential equation is to deal wit fuzzy dynamic systems. As classical differential equations, it is difficult to find the solutions to all fuzzy differential equations. In this paper an existence and uniqueness theorem for linear fuzzy differential equations is obtained. Moreover, the exact solution to linear fuzzy differential equation is given.

• Journal of The Korean Society of Agricultural Engineers
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• v.61 no.4
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• pp.11-22
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• 2019

The objective of this study was to improve the cross-sectional area and height estimation method using stream width. Stream water levels should be calculated together to simulate inundation of agricultural land. However, cross-sectional survey data of small rural rivers are insufficient. The previous study has developed regression equations between the width and the cross-sectional area and between the width and the height of stream cross-section, but can not be applied to a wide range of stream widths. In this study, cross-sectional survey data of 6 streams (Doowol, Chungmi, Jiseok, Gam, Wonpyeong, and Bokha stream) were collected and divided into upstream, midstream and downstream considering the locations of cross-sections. The regression equations were estimated using the complete data. $R^2$ between the stream width and cross-sectional area was 0.96, and $R^2$ between width and height was 0.81. The regression equations were also estimated using divided data for upstream, midstream and downstream considering the locations of cross-sections. The range of $R^2$ between the stream width and cross-sectional area was 0.86 - 0.91, and the range of $R^2$ between width and height was 0.79 ? 0.92. As a result of estimating the cross-sections of 6 rivers using the regression equations, the regression equations considering the locations of cross-sections showed better performance both in the cross-sectional area and height estimation than the regression equations estimated using the complete data. Hydrologic Engineering Center - River Analysis System (HEC-RAS) was used to simulate the flood stage analysis of the estimated and the measured cross-sections for 50-year, 100-year, and 200-year frequency floods. As a result of flood stage analysis, the regression equations considering the locations of cross-sections also showed better performance than the regression equations estimated using the complete data. Future research would be needed to consider the factors affecting the cross-sectional shape such as river slope and average flow velocity. This study can be useful for inundation simulation of agricultural land adjacent to an unmeasured stream.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.350-353
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• 1994

This paper presents a method to calculate the characteristic root areas and loci band of control systems with uncertainties. First, equations of boundary curves of root areas in the case of additive and multiplicative perturbation are derived. Then, an algorithm for the calculation of the array of closed curves is presented. When the upper bound of the absolute values of frequency responses for the uncertain part, is also frequency-dependent, the frequency-dependent, terms are included in the characteristic equation of the nominal system. This lead to the boundary equations of the root, areas for control systems with frequency-dependent uncertainty. Numerical examples of the control systems with multiplicative perturbations including frequency-dependent terms are presented to verify this calculation method. Finally, its applications to the design of robust control systems, e.g., passive adaptive control systems are also discussed.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1043-1048
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• 1990

The degenerate case of multivariable hyperbolic distributed-parameter systems (systems of hyperbolic partial differential equations) in time coordinate t and space coordinate x is characterized by a property that all the characteristic curves of the state equations are parallel to the coordinate axes of independent variables. It is a disturbing fact, although not well known, that the so-called maximum principle as applied to these systems does not exist for the control that depend on time alone. In this paper, however, it is shown that a set of necessary conditions in the small can exist for unconstrained as well as magnitude constrained controls in a locally convex set. The necessary conditions thus derived can be used conveniently to find the optimal control for degenerate hyperbolic distributed-parameter control systems.

• Structural Engineering and Mechanics
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• v.54 no.6
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• pp.1153-1174
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• 2015

Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.37-43
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• 1998

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.8
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• pp.1303-1308
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• 2003

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre-multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of ail relative coordinates, velocities, and accelerations. Since the coordinates, velocities, and accelerations are tightly coupled by the position, velocity, and acceleration level constraints, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all coordinates, velocities, and accelerations, which are coupled by the constraints. The position, velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The perturbed constraint equations are then simultaneously solved for variations of all coordinates, velocities, and accelerations only in terms of the variations of the independent coordinates, velocities, and accelerations. Finally, the relationships between the variations of all coordinates, velocities, accelerations and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent coordinate, velocity, and acceleration variations.